Filter for electrical oscillations

ABSTRACT

A filter for electric oscillations comprises n resonators, where n 4, which are coupled by line elements and have line characteristics. The filter has an input impedance which tends to zero on at least one side of the pass band, and also has a maximum at a given frequency, the echo attenuation in the pass band having more than one maximum. At least two of the echo attenuation poles occur at non-physical frequencies (po + OR sigma + j omega ). The absolute value of the real part ( sigma ) of the poles amounts to at least the nth part of the 3dB bandwidth of the filter.

United States Patent [191 Guenther Feb. 12, 1974 FILTER FOR ELECTRICALOSCILLATIONS [75] Inventor: Alfhart'Guenther, Haar, Germany PrimaryLlbermam Asslstanl Exammer-MarvIn Nussbaum [73] AssIgnee: SiemensAktiengesellschaft, Berlin & Attorney, A m, or Firm-Hill, Sherman,Meroni,

Munich, Germany Gross & Simpson [22] Filed: Mar. 19, 1973 i [57]ABSTRACT [21] Appl' 34249l A filter for electric oscillations comprises11 resonators, where n =4, which are coupled by line el- [30] ForeignApplication Priority Data ements and have line characteristics. Thefilter has an Man 23, 1972 Germany A p 22 14 2525 input impedance whichtends to zero on at least one I side of the pass band, and also has amaximum at a 52 us. 01. 333/72, 333/73 R given froquenoy, the echoattenuation in the p band 51 Int. Cl. H03h 9/26, H03h 13/00 having morethan one maximum. t eas two of the 58 Field of Search 333/71, 72, 73 R,30 R echo attenuation poles occur at -P y q cies (p 0' +jw). Theabsolute value of the real 5 References Cited part oof the poles amountsto at least the n' part FOREIGN PATENTS OR APPLICATIONS of the 3dBbandwidth Of the filter- 1,541,o75 12/1969 Germany 333/71 11 Claims, 5Drawing Figures FILTER FOR ELECTRICAL OSCILLATIONS BACKGROUND OF THEINVENTION 1. Field of the Invention This invention relates to filtersfor electric oscillations, and more particularly to filters whichcomprise a plurality of resonators which are coupled via line ele mentsand have line characteristics, which filters have an input impedancewhich tends towards zero at least on one side of the pass band and onthis side have an input impedance maximum at a given frequency and theecho attenuation of which possesses more than one maximum in the pasband.

2. Description of the Prior Art An occasional requirement in the designof filters is that an operative impedance maximum of the filter shouldoccur at a given frequency. As is known, in filters of conventionaldesign, for example filters operating in accordance with wave parametertheory or the so-called polynomial filters, such an operationalimpedance maximum occurs at an arbitrary frequency lying in the stopband of the filter. No attention is paid to this frequency state in thedesign of the filter, since only the other properties, such as e.g., themaximum permissible attenuation in the pass band and the blockingattenuation increase are the characterizing parameters. In the design offilters it is frequetly necessary to set the operational impedancemaximum at a specific, given fre quency positon if filters which wereinitially designed to be independent of one another are to be connectedto form a composite filter. German Pat. No. 1,902,091, as open toinspection, suggests setting the operational impedance maximum of onefilter at the center of the pass band of another. In the provision offilters having concentrated elements, this may be realized relativelysimply because a large number of circuit structures are available whichmay consist of concentrated elements and the number of possiblestructures includes at least one whose operational impedance maximumlies at the correct frequency position and also meets the otherconditions. In the provision offilters consisting of line elements suchas for example microwave filters or mechanical filters, the additionaldifficulty occurs that, dueto their physical nature, the line elementsemployed hae a compulsory predetermined electrical equivalent structureand cannot be interconnected with arbitrary freedom of form at aneconomical cost.

SUMMARY OF THE INVENTION An object of the invention is to providepossibilities of setting the frequency position of the operationalimpedance maximum in filters of the type described above and consistingof line elements without the other filter properties, as a consequence,suffering to an im practical extent.

The invention resides in the provision of a filter for electricoscillations comprising a plurality of resonators which are coupled vialine elements and have line characteristics, which filterhas an inputimpedance which tends towards zero at least on one side of the passband, and on this side has an input impedance maximum at a givenfrequency. The echo attenuation of the filter possesses more than onemaximum in the pass band, and the filter r resonators where n 5 4. Atleast two of the echo attenuation poles of the filter occur atnonphysical frequencies (p ia-iij w The absolute value of the real partlo' l of this complex echo attenuation pole positioning amounts to atleast the n part of the 3dB bandwidth 8,, of the filter.

BRIEF DESCRIPTION OF THE DRAWINGS Other objects, features and advantagesof the invention, its organization, construction ad operation will bebest understood from the following detailed description taken inconjunction with the accompanying drawings, on which:

FIG. 1 schematically illustrates the amechanical filter;

FIG. 2 graphically shows the distribution of zeros in thecomplexfrequency plane of conventional filters;

FIG. 3 graphically shows the distribution of zeros in the complexfrequency plane of filters in accordance with the invention;

FIG. 4 is a graphical illustration of the attenuation curves in a filterin accordance with the invention; and

FIG. 5 is a graph relating the operational input impedance withfrequency.

DESCRIPTION OF THE PREFERRED EMBODIMENT FIG. 1 shows a mechanical filteras an example of a filter consistinf of line elements. A characteristicof such filters is that the individual filter elements or at least partsof the individual filter elements do not consist of concentrated circuitelements such as coils and capacitors, but of elements which possessline characteristics and whose physical properties can be determined andcalculated with the aid of line theory. This applies both to theresonators of the filter and to the coupligs between the individualresonators. The same principles also apply to microwave filters inwhich, as is known, the geometrical dimensions of the individualelements, relative to the wave length, cannot be neglected so that theseelements also possess line characteristics.

The mechanical filter shown in FIG. 1 consists of a plurality ofresonators l, which are mechanically coupled to one another through acoupling element 2. In the exemplary embodiment, the resonators take theform of bending mode resonators, which is indicated by the oscillationmnodes marked 9. At the oscillating nodes, the filter can be supportedby elements, which are not shown in the drawing for the sake of clarity,which can be suitable support elements also secured, e.g., to a baseplate. The conversion of electrical energy into mechanical oscillatingenergy or the reconversion of the mechanical oscillating energy intoelectric energy takes place at the end resonators 3 and 3'. For thispurpose these end resonators are provided with respective elements 4 and4' which exhibit an electrostrictive eeffect and which are preferablymade of piezoceramic material. The electromechanical converter elements4 and 4', are secured in the conventional manner, for example bysoldering, to the end resonators and are provided on the area facingaway from the end resonators 3 and 3' with a thin metallization formingan electrode to which is conducted one of the two electric supply lines.The secondelectric supply line is directly connected to the metallicresonators and, for example, the piezoceramic plates 4 and 4' areprovided with a polarizing field running in the direction of thelongitudinal axis of the filter, i.e., therefore with a polarization inthe direction of the coupling element 2. If an electric construction ofalternating voltage is applied between the metallized electrode of theplate 4 and the resonator 3, the resonator is excited, via the so-calledcross-contraction effect, to bending mode oscillations in the directionof the double arrow 10, as long as its resonating frequency is at leastpaproximately equal to the frequency of the applied alternating voltage.These bending oscillations are transferred via the coupling element 2 tothe resonators l and to the second end resonator 3, where they arereconverted in converse fashion, via the piezoceramic plate 4 intoelectric oscillations.

As indicated in FIG. I by broken lines, capacitors 7 and 7' can beconnected in parallel respectively with the electromechanical converterelements 4 and 4, so that tthe static capacitance of the converterelements 4 and 4 may be increased. The individual converter elements maybe supplemented by adding coils 8 and 8 respectively in association withtthe capacitors 7 and 7 to form parallel resonance circuits. Theseparallel resonance circuits must be additionally taken intoconsideration in the calculation of the number n of filter circuits.

In the embodiment shown in FIG. 1, an additional mechanical coupling 6between the resonators 3 and 3 can also be provided to produce a pair ofattenuation poles.

The resonators 3 and 3 do not necessarily have to be connected and thecoupling can be co-phasal instead of in anti-phase as shown, as a resultof which the increase in gradient of the attenuation is replaced by aphase linearization. Such additional couplings are made betweenresonators which are not directly adjacent.

A mechanical coupling can be replaced by an electric coupling, indicatedin FIG. 1 by the capacitor shown in broken lineswhich is arrangedbetween the input converter and the output converter.

As already mentioned in the introduction, when designing filters inaccordance with the insertion loss theory, one commences from theso-called characteristic function and introduces the so-called complexfrequency p =o-+j was a frequency variable, wherein a is the real partand jw is the imaginary part. Here, the characteristic features of afilter are the positions of the zeros of the so-called characteristicfunction and the positions of the zeros of the so-called characteristicfunction and the positions of the zeros of the Hurwitz polynomial in thecomplex frequency plane. In filters which are constructed in accordancewith conventional known design processes, and which are designed withouttaking into account aspecial frequency state of the driving pointimpedance, the zeros of the characteristic function lie on the jw axis,whereas the zeros of the Hurwitz polynomial lie in the left P-halfplane. This distributiion is illustrated in FIG. 2 in which the zeros ofthe characteristic function are indicated by clots and the zeros of theHurwirz polynomial are indicated by crosses. As shown in FIG. 2, thezeris of the Hurwitz polynomial lie on locus which is very similar to anellipse and the 3dB bandwidth B is determined by the frequency band onthe jw axis which results ffrom the intersection points of thisimaginary ellipse with the j 'w axis. The zeros of the characteristicfunction simultaneously form the matching points in the pass band, whichis synonymous with the pole positions of the echo attenuation.

FIG. 3 shows the distribution of the positions of the zeros of thecharacteristic function and the Hurwitz polynomial in a filter designedin accordance with the invention. By way ofexample, the two echoattenuation poles ll, 11 are placed in such a manner that they occur atnon-physical frequencies, i.e., thus at the complex frequencies 1,,=i-o,, +j w,,-. Herc, attention should be paid that the absolute valuelo' lof the real part of this complex echo attenuation pole positioningamounts to at least the n part of the3dB bAndwidth B of the filter, inwhich n is the number of filter elements contained in the filter, plusany possible electric end circuits. As shown by the analysis of thisfilter, at least four resonators arerrequired for the realization of afilter in accordance with the invention.

When the distribution of the zeros is arranged in suitable fashion, asshown in FIG. 3, there are no distortions of the Tschebyscheffcharacteristic of the operational attenuation ripple, and the number ofwaves is only two lower than in a filter having the characteristicsshown in FIG. 2. This permits the frequency state of the driving pointimpedance maximum to be influenced, at a given bandwidth, pass ripplefactor and blocking flank gradient.

The detailed calculation of the circuit elements takes place inaccordance with known methods. The following explanations refer to theexample of a symmetrical filter.

The characteristic function K of a symmetrical filter with tthe chainmatrix is a function of the filter elements E K= (BC) /2 2 K (E,, EE,,,).

in which 1 is a numerical variable between the numbers 1 and m.

In a a n grade filter, the characteristic function is a parabola of then grade, and is therefoe characterized by m =nl features (curve points,end points, inflection points etc.). With very good approximation, thisallso applies to filters including lineresonators, if the higherinherent frequencies are far removed and this is generally the case. Anumber m filter elements which are independent of one another arerequired for the realization of a characteristic function with mfeatures. The total differential of the characteristic function, withregard to the elements is m N dK 21 d v and, replacing the differentialsby differences "I AK E aiAEv-l-R When the nonlinear remaining power R issmall, AK represents the deviation from the theoretical behavior andAE,, the necessary element modifications; the sensitivities 8K/8E, aredetermined by analysis. A numbew squat saspithistype areres iredwh Fag.Kis interpreted in the first and second equation as lower and upper bandedge, in the third and fourth as rear and imaginary part of the complexecho atte'iiuation'pole attains; disarm-2i equations as an extreme valeof the characteristic function. Generally the process converges after afew iterations.

Filters designed in accordance with the above statements also have thefollowing properties:

The circuit grade has apparently been reduced by two, and the flankgradient reduces somewhat however, in no way corresponding to areduction in grade by two -the overall decrease being variouslydistributed between the two flanks. The closer to the band edge theengagement takes place, the more the adjacent flank is weakened and theless the opposite flank is weakened, and the maxima of thedriving pointimpe dance below and above the band edges move from lower to higherfrequencies, if theunification of the attenuation maxima, commencing atthe lower band edge, is effected step by step at higher three-unitgroups.

With a filter designed for a pass band of 48.3 to 51.4 kHz, thefollowing tabulated figures result.

Tonvergence of the a wave group Position of (W/Z),,,,,

The term a wave group is to be understood as the number of extremesoccurring in the pass band between the matching points. The value(W/Z),, is the quotient of the input driving point impedance maximum anda reference impedance Z, which will be explained with reference to FIG.5.

A fine adjustment of the impedance maximum is possible by detuning theelectric end circuits in such a manner that the total of detuningsamounts to zero; the distortion of the transmission behavior is thenminimal. The mechanical body of the filter can havethe complete elementsymmetry which is favorable from theproduction point of view.

The abovedescribed arrangement may be modified by unifying two or moreecho attenuation poles, resulting in a multiple, but real, zeropositioning of the characteristic function.

The above-described filter is preferably used in systems in whichrelatively high requirements are placed on the properties of the filter,and therefore it may be used with particular advantage for filters incarrier frequency units. As is known, in these cases theaudio bandwidthis approximately 3 kHz, so that bandwidths of morethan 2 kHz areparticularly favorable for the described filter.

TThe filter may be designed with unsteepened attenuation characteristic,for example with Chebyshev characteristic, at any rate a nonmonotonous,monotonous, attenuation behavior in the pass band. In accordance withthe invention, the end circuits are provided with a bandwidth 8,, whichsatisfies the condition B1 2 0.3366 (1 w)/(l +W) n8 wherein and a is thegeometric m ean of theihser'ti'dfid' 'r'ib ple, expressed in nepers, inthe pass band, after deduction of the loss attenuation caused by thefinal values of th e resonators. This is represented in detail in FIG.

4, in whi cj theinsertion loss a =a +a,,, plotted against ithe frequencyfis shown by the solid curve 14. The dot ted curve 15 shows the courseof the loss attenuation a, in dependence upon the frequency and thesolid curve 16 shows the filter attenuation a,,, whose maxima are a Withthe use of reactance bridges, attenuation poles at finite frequenciesmay be produced or poles at com plex frequencies to influence the groupdelay. Reactance bridges of this kind are realized, for example in FIG.1, by an electric circuit element such as, e.g., the capacitor 5, or bya mechanical line such as, e.g., the coupling 6 leading from theresonator 3 to the resonator 3. Here, in a simiilar way to the couplingelement 2 which codetermines the filter bandwidth, the mechanicalcoupling element 6 executes longitudinal oscillations. Bridges, such asthose shown in FIG. 1, from end circuit to end circuit possesstheadvantage that they do not substantially influence the filterbehavior in the pass band in practice, and yet clearly increase thegradient of the stop band. They have theadvantage that they consequentlydo not require to be taken into account in the dimensioning of thefilter, and only require to be applied subsequently for the fineadjustment. The end circuits, i.e., thus either the resonators 3, 3' inasso ciation with the converters 4, 4, or the electric end circuitsformed from, concentrated circuit elements and consisting of thecapacitors 7, 7, and the coils 8, 8, are so dimensioned that theitheirbandwidth b satisfies the condition 3, a 0.366 (l w)/(] +W) nB In FIG.5, the ratio W/Z between driving point input impedance and a referenceimpedance, in particular the terminating impedance Z, is plotted independence upon the frequency. In thepass band DB of the filter, thisimpedance ratio has an approximate value of 1 and exhibits anapproximate Chebyshev behavior. The broken line is to indicate thatfilters with an arbitrary number n of filter resonators can be employed,since, as is known, the number of maxima and minima occurring in thepass band DB depend upon the number of resonance circuits employed.Outside the pass band, i.e., at a predeterminable frequency f,,, thedriving point input impedance ratio W/Z possesses a maximum and thismaximum may in fact be freely selected by tehe described dimensioningrules within relatively wide frequency limits.

Although I have described my invention by reference to a specificillustrative embodi embodimentt, many changes and modifications thereofmay become appar ent to those skilled in the art without departing fromthe spirit and scope of the invention. 1 therefore intend to includewithin the patent warranted hereon, all such changes and modificationsas may reasonably ad properly be included within the scope of mycontribution to the art.

I claim:

1. A filter for electric oscillations comprising a plurality ofresonators which have line characteristics, line elements coupling saidresonators, said filter having input impedance which tends towards zeroat least on one side of its pass band, and on this side has an inputimpedance maximum at a given frequency, and the echo attenuation of thefilter possessing more than one maximum in the pass band, wherein saidfilter comprises n resonators, where n =4 l at least two echoattenuation poles occurring at non-physical frequencies (p, =io- +j mand the absolute value of the real part o'l) of this complex echoattenuation pole positionand a is the geometric mean of the insertionloss ripple, expressed in nepers, in the pass band, after thesubtraction of the loss attenuation due to the finite Q- factors of theresonators.

4. A filter as claimed in claim 1, wherein said resonators aremechanical resonators which are mechanically coupled to one another.

5. A filter as claimed in claim 1, wherein there is pro-' vided areactance bridge from the first to the last resonator and the bandwidthB of its end circuits satisfies the equation B 0.366 (lW)/( l+W)- nB,,.

6. A filter as claimed in claim 5, wherein said resonators aremechanical resonators which are mechanically coupled to one another.

7. A filter as claimed in claim 6, wherein the reactance bridge is amechanical line.

8. A filter as claimed in claim 6, wherein the reactance bridge is aconcentrated circuit element.

9. A filter as claimed in claim 1, wherein at least one of the endresonators is a resonant circuit consisting of concentrated circuitelements.

10. A filter as claimed in claim 9, wherein saidresonators are arrangedsymmetrically and wherein the two electric end circuits are made up ofelements having different dimensions.

11. A filter as claimed in claim 1, wherein said resonators are in theform of bending mode oscillators and the coupling elements are in theform of longitudinal mode couplers.

V UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION 3,792, 382 DateFebruag 12, 1974 Alfhart Gue nther Patent No.

Inventor(s) It is certified that error appears in the above-identifiedpatent and that said Letters Patent are hereby corrected as shown below:

Read the application No. "342, 491" as 342, 4 31".

Signed and sealed this 24th day of Deoember 1974.

(SEAL) Attest c. MARSHALL DANN MCCOY M. GIBSON JR.

Commissioner of Patents Attesting Officer FORM PO-1050 (10- USCOMM-DCscam-P69 US, GOVERNMENT PRINTING OFFlCEt I9 55 0-365-334

1. A filter for electric oscillations comprising a plurality ofresonators which have line characteristics, line elements coupling saidresonators, said filter having input impedance which tends towards zeroat least on one side of its pass band, and on this side has an inputimpedance maximum at a given frequency, and the echo attenuation of thefilter possessing more than one maximum in the pass band, wherein saidfilter comprises n resonators, where n 4 at least two echo attenuationpoles occurring at non-physical frequencies (po + OR - o + j o) and theabsolute value of the real part ( sigma ) of this complex echoattenuation pole positioning amounts to at least the nth part of the 3dB bandwidth Bo of the filter.
 2. A filter as claimed in claim 1,wherein the bandwidth of the filter is greater than 2 kHz.
 3. A filteras claimed in claim 1, wherein the attenuation characteristic is notsteepened by finite attenuation poles and the bandwidth B1 of its endcircuits satisfies the equation B1 > or = 0.366 (1- w)/(1+ w). nBo,where e
 4. A filter as claimed in claim 1, wherein said resonators aremechanical resonators which are mechanically coupled to one another. 5.A filter as claimed in claim 1, wherein there is provided a reactancebridge from the first to the last resonator and the bandwidth B1 of itsend circuits satisfies the equation B1 > or = 0.366 (1-w)/(1+w). nBo. 6.A filter as claimed in claim 5, wherein said resonators are mechanicalresonators which are mechanically coupled to one another.
 7. A filter asclaimed in claim 6, wherein the reactance bridge is a mechanical line.8. A filter as claimed in claim 6, wherein the reactance bridge is aconcentrated circuit element.
 9. A filter as claimed in claim 1, whereinat least one of the end resonators is a resonant circuit consisting ofconcentrated circuit elements.
 10. A filter as claimed in claim 9,wherein said resonators are arranged symmetrically and wherein the twoelectric end circuits are made up of elements having differentdimensions.
 11. A filter as claimed in claim 1, wherein said resonatorsare in the form of bending mode oscillators and the coupling elementsare in the form of longitudinal mode couplers.